Work

Equations over Finite Monoids with Infinite Promises

Year: 2026

Type: article

Abstract: Larrauri and Živný [ICALP’24/ACM ToCL’24] recently established a complete complexity classification of the problem of solving a system of equations over a monoid \({N}\) assuming that a solution exists over a monoid \({M}\) , where both monoids are finite and \({M}\) admits a homomorphism to \({N}\) . Using the algebraic approach to promise constraint satisfaction problems, we extend their complexity classification in two directions: we obtain a complexity dichotomy in the case where arbitrary relations are added to the monoids, and we moreover allow the monoid \({M}\) to be finitely generated.

Source: ACM Transactions on Computational Logic

DOI: 10.1145/3816149

Authors: Alberto Larrauri, Antoine Mottet, Stanislav Živný

Institutions: Universidad de Zaragoza, Hamburg University of Technology, University of Oxford

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funder: UK Research and Innovation

Awards: G4136533573, G8702647912